Squares:9600s

9600

4-cycle (see 1600).

9600² = 92160000, 1600² = 02560000, 5600² = 31360000, 3600² = 12960000,
Other examples: 2916 - 5030 - 3009 - 0540 - 2916, and 2100 - 4100 - 8100 - 6100 - 2100.

10⁴ + 9600 = 140², 10⁴ - 9600 = 20².

Page of Squares : First Upload October 6, 2008 ; Last Revised August 9, 2011
by Yoshio Mimura, Kobe, Japan

9602

9602⁵ = 81622239812813568032 :
8² + 1² + 6² + 2² + 22² + 39² + 8² + 1² + 28² + 13² + 5² + 6² + 80² + 3² + 2²
= 8² + 1² + 6² + 22² + 2² + 39² + 8² + 1² + 28² + 13² + 5² + 6² + 80² + 3² + 2²
= 8² + 1² + 6² + 2² + 2² + 2² + 39² + 8² + 1² + 2² + 81² + 35² + 6² + 8² + 0² + 3² + 2²
= 8² + 1² + 6² + 2² + 2² + 2² + 39² + 81² + 2² + 8² + 1² + 35² + 6² + 8² + 0² + 3² + 2²
= 81² + 6² + 2² + 2² + 2² + 39² + 8² + 1² + 2² + 8² + 1² + 35² + 6² + 8² + 0² + 3² + 2² = 9602.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9603

9603² = 92217609, and 9² + 2² + 2² + 1² + 7² + 6² + 0² + 9² = 16².

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9604

The square of 98.

Komachi equations:
9604² = 9⁴ * 8⁴ * 7⁴ / 6⁴ / 54⁴ * 3⁴ * 21⁴ = 98⁴ + 7⁴ - 6⁴ / 54⁴ * 3⁴ * 21⁴
= 98⁴ + 7⁴ / 6⁴ * 54⁴ - 3⁴ * 21⁴ = 98⁴ + 7⁴ / 6⁴ * 54⁴ / 3⁴ - 21⁴
= 98⁴ - 7⁴ + 6⁴ / 54⁴ * 3⁴ * 21⁴ = 98⁴ - 7⁴ / 6⁴ * 54⁴ + 3⁴ * 21⁴
= 98⁴ - 7⁴ / 6⁴ * 54⁴ / 3⁴ + 21⁴ = 98⁴ * 7⁴ / 6⁴ * 54⁴ / 3⁴ / 21⁴
= 98⁴ / 7⁴ * 6⁴ / 54⁴ * 3⁴ * 21⁴.

Page of Squares : First Upload October 6, 2008 ; Last Revised November 29, 2010
by Yoshio Mimura, Kobe, Japan

9607

9607² = 92294449, a square with just 3 kinds of digits.

9607² = 92294449 with 9229444 = 3038² and 9 = 3³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9608

9608² = 2⁴ + 14⁴ + 14⁴ + 98⁴.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9609

Komachi equation: 9609² = 98⁴ + 7⁴ - 6⁴ + 54⁴ / 3⁴ - 2⁴ - 10⁴.

Page of Squares : First Upload November 29, 2010 ; Last Revised November 29, 2010
by Yoshio Mimura, Kobe, Japan

9611

9611² = 98³ + 337³ + 376³.

1 / 9611 = 0.00010404...., and 10404 = 102².

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9612

9612² = (1² + 8)(2² + 8)(9² + 8)(98² + 8) = (9² + 8)(10² + 8)(98² + 8).

9612² = 18³ + 34³ + 452³ = 18³ + 108³ + 450³ = 93³ + 283³ + 410³.

Page of Squares : First Upload October 6, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9614

1 / 9614 = 0.000104014978156, 10² + 4² + 0² + 14² + 9² + 78² + 1² + 56² = 9614,
1 / 9614 = 0.000104014978156, 10² + 4² + 014² + 9² + 78² + 1² + 56² = 9614.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9615

The square root of 9615 is 98.056106...., and 98 = 0² + 5² + 6² + 1² + 0² + 6².

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9617

9617² = 98.0663041...., and 98 = 0² + 6² + 6² + 3² + 0² + 4² + 1².

9617⁵ = 82261775754871227857 :
8² + 22² + 6² + 17² + 7² + 5² + 7² + 5² + 4² + 87² + 12² + 27² + 8² + 5² + 7² = 9617.

Page of Squares : First Upload October 6, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9619

9619² = 92525161, a zigzag square.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9620

9620² = (1² + 1)(2² + 1)(3² + 1)(5² + 1)(6² + 1)(31² + 1) = (1² + 1)(5² + 1)(31² + 1)(43² + 1)
= (1² + 1)(5² + 1)(6² + 1)(7² + 1)(31² + 1)
= (12² + 4)(16² + 4)(49² + 4) = (3² + 4)(4² + 4)(12² + 4)(49² + 4).

1378^k + 3354^k + 4446^k + 7722^k are squares for k = 1,2,3 (130², 9620², 767260²).

Page of Squares : First Upload July 18, 2011 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9621

9621² = 92563641, and 9256 + 364 + 1 = 9621.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9624

9624² = 24³ + 64³ + 452³ = 176³ + 324³ + 376³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9625

9625² = (1² + 6)(7² + 6)(13² + 6)(37² + 6).

9625² = (138 + 139 + 140 + 141 + 142)² + (143 + 144 + 145 + 146 + 147)² + (148 + 149 + 150 + 151 + 152)² + ... + (383 + 384 + 385 + 386 + 387)².

9625² = 92640625 with 9 = 3² and 2640625 = 1625².

Page of Squares : First Upload October 6, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9627

9627⁵ = 82690355506816316907 :
8² + 26² + 9² + 0² + 35² + 5² + 50² + 68² + 1² + 6² + 3² + 16² + 9² + 0² + 7²
= 8² + 26² + 9² + 0² + 35² + 5² + 50² + 68² + 16² + 3² + 1² + 6² + 9² + 0² + 7² = 9627.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9628

9628² = 4⁴ + 52⁴ + 52⁴ + 94⁴.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9631

9631² = 92756161, a zigzag square.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9632

9632² = (3² + 7)(6² + 7)(7² + 7)(49² + 7).

Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9633

9633² = 100³ + 182³ + 441³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9638

9638²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

9639

9639² = (41 + 42 + 43 + ... + 103)² + (104 + 105 + 106 + ... + 166)².

Page of Squares : First Upload October 9, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

9640

9640² = 4³ + 244³ + 428³ = 66³ + 352³ + 366³.

9640² = 92929600, and 9 + 29 + 2 + 9600 = 9640.

9640⁵ = 83250177761382400000 :
8² + 3² + 2² + 50² + 17² + 77² + 6² + 13² + 8² + 24² + 0² + 0² + 0² + 0² + 0² = 9640.

Page of Squares : First Upload October 6, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9642

9642² = 92968164, a zigzag square.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9643

9643² = 12⁵ + 14⁵ + 20⁵ + 25⁵ + 38⁵.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9645

9645² = 57³ + 284³ + 412³ = 102³ + 217³ + 434³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9646

9646 = (1² + 2² + 3² + ... + 52²) / (1² + 2²).

Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

9648

9648² = 66³ + 174³ + 444³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9649

The square root of 9649 is 98.2293...., and 98 = 2² + 2² + 9² + 3².

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9654

9654² = 93199716, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

9657

The square root of 9657 is 98.270036...., and 98 = 2² + 7² + 0² + 0² + 3² + 6².

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9658

9658² = 31³ + 66³ + 453³.

9658⁵ = 84030317662107364768 :
8² + 4² + 0² + 3² + 0² + 3² + 1² + 7² + 6² + 62² + 10² + 73² + 6² + 4² + 7² + 6² + 8² = 9658.

Page of Squares : First Upload October 6, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9659

1 / 9659 = 0.0001035303861683, 10² + 3² + 5² + 30² + 38² + 6² + 16² + 83² = 9659.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9660

9660sup>2 = (3² + 5)(5² + 5)(15² + 5)(31² + 5).

9177^k + 9660^k + 11454^k + 12558^k are squares for k = 1,2,3 (207², 21597², 2270997²).

The integral triangle of sides 12025, 15617, 20742 has square area 9660².

Page of Squares : First Upload July 18, 2011 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9664

9664² = (5² + 7)(12² + 7)(139² + 7).

Page of Squares : First Upload October 6, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9665

9665² = 93412225, and 9² + 3² + 4² + 1² + 2² + 2² + 2² + 5² = 12².

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9666

9666² = 142³ + 285³ + 407³.

9666⁵ = 84378918376513260576 :
8² + 4² + 3² + 7² + 8² + 9² + 1² + 8² + 37² + 65² + 1² + 3² + 2² + 60² + 5² + 7² + 6²
= 8² + 4² + 37² + 8² + 9² + 1² + 8² + 3² + 7² + 65² + 1² + 3² + 2² + 60² + 5² + 7² + 6² = 9666.

Page of Squares : First Upload October 6, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9667

9667² = 153³ + 280³ + 408³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9668

9668² = 8⁴ + 28⁴ + 28⁴ + 98⁴ = 9⁵ + 12⁵ + 16⁵ + 18⁵ + 39⁵.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9669

9669² = 93489561, and 9 * 3 * 4 * 89 + 56 + 1 = 9669.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9671

9671² = 20⁴ + 70⁴ + 73⁴ + 80⁴.

9671² = 93528241, a zigzag square.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9672

9672² = 93547584, a zigzag square.

9672² = (1² + 3)(3² + 3)(6² + 3)(11² + 3)(20² + 3).

Page of Squares : First Upload October 6, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9673

9673² = 38⁴ + 43⁴ + 76⁴ + 86⁴ = 46⁴ + 64⁴ + 76⁴ + 79⁴.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9675

9675² = 65³ + 240³ + 430³.

9675² = 93605625, and 9360 + 5 + 62 * 5 = 9360 + 5 * 62 + 5 = 9675.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9680

9680² = 36³ + 248³ + 428³ = 44³ + 297³ + 407³ = 176³ + 330³ + 374³.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9682

9682²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

9683

9683⁵ = 85123536687877648643 :
8² + 5² + 12² + 3² + 53² + 66² + 8² + 7² + 8² + 7² + 7² + 6² + 4² + 8² + 6² + 43² = 9683.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9685

9685⁵ = 85211483303667053125 :
85² + 21² + 14² + 8² + 3² + 3² + 0² + 3² + 6² + 6² + 7² + 0² + 5² + 31² + 25² = 9685.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9686

9686² = 93818596, a zigzag square.

9686² = 93818596, and 9² + 3² + 8² + 1² + 8² + 5² + 9² + 6² = 19².

9686⁵ = 85255483862113038176 :
8² + 5² + 2² + 5² + 54² + 8² + 3² + 8² + 62² + 1² + 1² + 30² + 38² + 17² + 6²
= 8² + 5² + 2² + 5² + 54² + 8² + 38² + 62² + 1² + 1² + 30² + 3² + 8² + 17² + 6² = 9686.

Page of Squares : First Upload October 6, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9687

9687² = 2⁴ + 4⁴ + 48⁴ + 97⁴.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan

9690

The integral triangle of sides 6205, 35587, 39208 (or 27455, 117064, 144481) has square area 9690².

Page of Squares : First Upload October 21, 2011 ; Last Revised October 21, 2011
by Yoshio Mimura, Kobe, Japan

9691

9691² = 93915481, a zigzag square.

Page of Squares : First Upload October 6, 2008 ; Last Revised October 6, 2008
by Yoshio Mimura, Kobe, Japan